Dynamics in multicomponent systems

本项目的重点是时间相关的密度矩阵重整化群方法来模拟光学晶格中强关联的一维超冷玻色子和费米子量子气体的动力学，特别强调多组分系统。我们将继续我们的调查使用超晶格加载两种玻色子系统，观察磁动力学远离超晶格中的平衡，以及所需的平衡态的绝热状态制备的产生。在类似的多物种玻色系统中，我们将研究玻色旋量凝聚体在晶格结构上发生变化的动力学（六边形与三角形）和自旋态相关势。我们还将考虑具有有趣的非平衡或弛豫物理的单组分玻色子系统：重点将放在特殊图案加载玻色一维链的弛豫和耦合玻色阶梯中的量子多体Landau-Zener效应。前者是一个控制良好的玩具模型，用于非平凡封闭量子系统中的弛豫，后者是一个类似的控制良好的模型，用于量子多体系统中的绝热状态转换。在费米子系统中，我们将专注于自旋不平衡和质量和自旋不平衡系统中的FFLO物理（稳定性，膨胀动力学）。我们将对关闭限制陷阱后的一维费米子系统的膨胀进行广泛的研究，并根据原始量子相位分析no，弹道或扩散输运的出现。（特别是在无序系统中，其中在释放时预期局部化现象），模型的可积性，并从总体上研究了这种扩展方法在表征量子多体态方面的潜力。在方法学方面，我们将研究新的建议，将时间相关的DMRG的范围扩展到更长的时间尺度，主要是通过切换到海森堡图像，更好地理解长时间尺度上的典型弛豫问题，并提取相互作用的量子多体系统中弛豫的解析关系。这将与有限系统中所需状态的高保真度与所需观测量的高保真度之间联系的一般概念研究有关：对后者的要求将在实验上系统地不那么严格。

This project focuses on the time-dependent density-matrix renormalization group method to simulate the dynamics of strongly correlated one-dimensional ultracold bosonic and fermionic quantum gases in optical lattices with a special emphasis on multicomponent systems. We will pursue our investigations of the use of superlattices loaded with two-species bosonic systems to observe magnetic dynamics far from equilibrium in superlattices as well as the generation of desired equilibrium states by adiabatic state preparation. In similar multispecies bosonic systems, we will investigate the dynamics of bosonic spinor condensates undergoing changes in the lattice structure (hexagonal vs. triagonal) and spin-state dependent potentials.We will also consider single-component bosonic systems with interesting out-of-equilibrium or relaxation physics: the focus will be on the relaxation in special pattern-loaded bosonic one-dimensional chains and the quantum many-body Landau-Zener effect in coupled bosonic ladders. Whereas the former is a well-controlled toy model for relaxation in a non-trivial closed quantum system, the latter is a similarly well-controlled model for adiabatic state transformations in quantum many-body systems.In fermionic systems, we will be focussing on the FFLO physics (stability, expansion dynamics) both in spin-imbalanced and mass- and spin-imbalanced systems. We will carry out extensive studies on the expansion of 1D fermionic systems after switching off the confining trap and analyze the emergence of no, ballistic or diffusive transport depending on the original quantum phase (in particular in disordered systems, where localization phenomena are expected upon release), the integrability of the model, and generally investigate the potential of this expansion method for the characterization of quantum many-body states.On the methodological side, we will be investigating new proposals to extend the reach of time-dependent DMRG to longer time-scales, mainly by switching to a Heisenberg picture, to get a better understanding of typical relaxation problems on long time scales and extract analytical relations for relaxation in interacting quantum-many body systems. This will be related to general conceptual studies of the link between high fidelity for desired states vs. high fidelity in desired observables in finite systems: the requirements for the latter will be systematically less stringent experimentally.